MHB How Can You Test for Symmetry in Mathematics?

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To test for symmetry in mathematics, one can evaluate functions for symmetry about the x-axis, y-axis, and origin. The function y = 2x - 4 is analyzed, revealing it is not symmetric about the y-axis or the origin. When substituting -x into the function, the resulting expression does not match the original, confirming a lack of symmetry. The discussion emphasizes the importance of applying specific rules for testing symmetry in algebraic functions. Overall, understanding these symmetry tests is crucial for analyzing mathematical graphs.
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Test for symmetry about the x-axis, y-axis and origin.

| y | = 2x - 4

What are the rules for testing for symmetry?
 
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RTCNTC said:
Test for symmetry about the x-axis, y-axis and origin.

| y | = 2x - 4

What are the rules for testing for symmetry?

... have you researched "testing graphs for symmetry" ?

Algebra - Symmetry
 
Great! I will answer both symmetry questions tomorrow. Going to work now.
 
| y | = 2x - 4

| -y | = 2x - 4

y = 2x - 4

Symmetric about the x-axis?

| y | = 2(-x) - 4

| y | = -2x - 4

| y | = -2x - 4

Not symmetric about the y-axis.

| y | = 2x - 4

| -y | = 2(-x) - 4

y = -2x - 4

Not symmetric about the origin?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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